Some of my experience isn't replicable; As I said, I've been doing this for 15 years professionally. I also have a near-photographic memory for books (which is a real pain when I want to re-read, especially mysteries) and I've read approximately 20,000 children's books so I have a huge database in my head. My library is large enough to have a decent budget but small enough that I can keep track of everything I buy - approximately 2,500 items per year.
Of course, you can't just sit on the budget while you follow my marvelous advice, so for your first year or two stick to purchasing obviously popular series and subjects (Dogman, vehicle picture books, animals), award-winners and starred reviews, and specifically requested titles.
My first advice is to get to know your community, your schools, and your audience. This is not a one-time thing as all of these elements will evolve over time. You'll also have to decide what amount of weight to put on different needs and requests. If only one or two people are asking for something, is it worth purchasing? Will it be popular with other patrons? Will it balance out a section of the collection? Spend time talking to patrons and kids and find out what they're interested in and what their favorite series are, but make sure you're not only getting the viewpoints of a handful of vocal patrons. Do you have a big homeschooling population that wants older/classic titles? Do you have a lot of struggling readers and need a broad range of beginning chapters and early readers? What nonfiction subjects are popular? What subjects are assigned in school? Does the school use assigned reading lists? If you can connect with a school librarian and/or teachers, you can get to know their curriculum; for example, most of my fourth grades study the American Revolution at some point so I've beefed up that collection - but it also circulates on its own and to homeschool groups. The "100 page biography at your reading level" is thankfully a thing of the past, so I've moved away from purchasing biographies to fill that need. My school district has access to a wide range of databases, so I don't spend $$$ on the nonfiction sets, especially the country/state ones that are a huge money sink. This is an ongoing process that you should be doing continually and constantly when you're at work. Not when you're not at work, unless you find it a personally relaxing occupation.
Next, get to know your collection. While I do run reports to weed, I prefer to physically touch each book as it helps me remember what we've got as well as looking at condition. You may not want to touch your books, in which case it's probably time for some serious replacements, or you may have more important things to store in your brain than 27,000 titles and covers, which is totally fine! But you should regularly spend time physically with the collection - look at the shelving carts and see what is circulating, review displays to see what is being taken, look at the shelves to see which are the messiest, i.e. the most used. Are sections dusty and neglected? Are shelves crammed with books? Do the books pulled for display look in good condition?
That's the physical side of it - the data I'll address more in the fourth and final part of this series, but use your reporting software, if you have any, to see statistics on what is circulating, what's sitting on the shelf, what is being lost/stolen. Look at collections sizes - do you have a huge amount of board books, compared to picture books? Does your nonfiction average forty years old? I don't personally do diversity audits, but they can be another tool to get to know your collection; you may also have reports available that will give you an idea of distribution of subject and genre. If your collection as an average dates back twenty years or more, you don't need a diversity audit - it's almost certainly not diverse.
Now that you are appropriately daunted by the lifetime of work you have taken on in building and maintaining a mid-sized youth collection, let's move on to some resources to help you do this.